Chets Creek Elementary is a K-5 professional learning community with 1,300 learners in Jacksonville, FL. Coaching Chronicles was first created when I served as the school's Instructional Coach (2004-2011). I have since served as a third grade learning leader(2011-2013), and am now the school's Assistant Principal. Regardless of my role, this blog shares snippets of our learning journey and Creek Life.

Saturday, October 6, 2012

Math Portfolio Piece, Addition Strategies

Addition Strategies

From
time to time, we have students complete math portfolio pieces to show
evidence of students' understanding of a concept or skill. Recently,
students completed an addition strategy piece.

The portfolio piece had two problems, 298+574, and a word problem, Mrs.
Shall has 321 shells in her seashell collection. Miss Russell has 524
shells in her seashell collection. How many seashells do Mrs. Shall and
Miss Russell have if they combine their collections?

Students
used two different strategies to solve. Research shows that when
students make a computational error and use the same strategy the second
time they solve, they commonly make the same mistake. In addition,
students with a tool box of strategies are better able to approach each
problem and use the strategy that is most efficient for the given
problem. In
some situations, the most efficient strategy is the traditional
algorithm, but in others, to use more mental math, it may be
compensation or left to right addition.

This
is a student's sample from our Addition Portfolio Piece. You'll notice
that the student used two different strategies to solve 298+574, decomposing by place value and left to right addition. Decomposing By Place Value298+574(200+500) + (90+70) + (8+4) 700 + 160 + 12 = 872

Decomposing
by place value is a strategy used by many mathematicians for mental
math. The strategy keeps the place value of the numbers, and gives
students the opportunity to solve for partial sums by place value. The
strategy, in this situation, avoided the traditional regrouping between
place values. You can see the student's understanding of correct
algebraic notation, too. Left to Right Addition 298+574 700+ 160 12 872

Like
decomposing, left to right is a strategy that lends itself to mental
math, and keeps the place value of numbers in perspective. You'll notice
the student's partial sums are recorded by place value, too. Again,
the student has avoided the traditional strategy of regrouping that the
traditional algorithm demands in this equation.

Compensation / Creating an Equivalent ProblemIn
the second problem, the student also shows his command of at third
strategy, compensation. He solves 321+524 by creating an equivalent
problem, 321+524 = 330+ 515.

321 (+9) 330+ 524 (-9) 515 845

When
compensating, students create an equivalent problem using landmark
numbers. Students can easily solve 330+515 without pencil and paper. Many of the students on this portfolio piece used compensating for the first problem, too, 298+574.
Compensating to create the equivalent problem 300+572 makes solving the
problem so much easier. This type of flexibility in thinking is exactly
what adults with good number sense do on a daily basis. 298 (+2) 300 + 574 (-2) 572 872

Traditional AlgorithmWe
don't avoid the traditional algorithm, but we do insist that students
correctly explain it when they solve. In the second problem many
students used the traditional algorithm. This strategy was very
efficient because it did not require any regrouping. 321+ 524 845 A few students used the traditional algorithm for the first problem which did require regrouping. 11 298+574 872

When
using this strategy students should be able to explain, "Eight plus
four equals 12, I regroup 10 ones and create another group of ten. One
group of ten, plus 9 groups of ten, plus seven groups of ten equals 18
groups of ten. I make one group of 100 out of 10 groups of 10. One
group of 100, plus 2 groups of 100, plus 5 groups of 100, equals 8
groups of 100. My sum is 872."

Students
reach this level of abstract math understanding by first exploring
other strategies. One of the earliest strategies students explore is the
open number line.

Open Number Line

The
open number line is a concrete strategy that third grade students
commonly revert to, particularly when they get stuck, or have
conflicting sums in two different strategies. When using the open
number line, we encourage students to start with the largest addend and
then add on. We also encourage them to make the fewest jumps possible.
One way of jumping on the open number line is provided in this example.

Regardless
of a student's strategy, we are working toward efficiency, flexibility,
and good number sense. We know that exposing them to many strategies
will assist them in reaching this goal.